Local monotonicity formulas for some nonlinear diffusion equations

Ecker, Klaus
May 2005
Calculus of Variations & Partial Differential Equations;May2005, Vol. 23 Issue 1, p67
Academic Journal
The article presents information on local monotonicity formulas for some nonlinear diffusion equations. Another closely related equation is the mean curvature flow of submanifolds. Common to all these equations is the fact that they arise as gradient flows for certain energy densities. Monotonicity formulas involving the associated energy densities for the first two equations were derived. It is the main purpose of this paper to discuss these formulas in detail and establish localised versions. A description of the corresponding results for the mean curvature flow will also be discussed.


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